prime number dedector

 Design a digital circuit that turns on LED when 1, 2, 3, 5, 7, 11, 13 causes on a 4 bit data bus.

              

Here we are going to design a digital circuit that glows an LED when prime numbers till 16 is “ON” on a 4 bit data bus. To design such circuit, the apparatus required are:

APPARATUS:

1.  IC 7408, 7432, 7402.

2.  4 10K Ohm resistor.

3.  9 volt battery.

4.  4 dip switches for input.

5.  1 LED.

STEP 1:

To design a digital circuit, the first thing to do is to make a Truth Table. Following Truth Table will be made in order to achieve our task.

D	C	B	A	Y
0	0	0	0	1
0	0	0	1	1
0	0	1	0	1
0	0	1	1	0
0	1	0	0	1
0	1	0	1	0
0	1	1	0	1
0	1	1	1	0
1	0	0	0	0
1	0	0	1	0
1	0	1	0	1
1	0	1	1	0
1	1	0	0	1
1	1	0	1	0
1	1	1	0	0
1	1	1	1	0

The equation obtained from the above Truth Table is following:

Y= D’.C’.B’.A’+D’.C’.B’.A+D’.C’.B.A’+D’.C.B’.A’+D’.C.B.A’+

D.C’.B.A’+D.C.B’.A’

Now from the above equation we will make a Karnaugh Map.

STEP 2:

The second step is to make a Karnaugh Map so that we can simplify our complicated Boolean Expression. Following Karnaugh Map will take place.

	C’D’	C’D	CD	CD’
A’B’
A’B	1
AB	1	1		1
AB’	1		1	1

From Karnaugh Map, we get the following simplified form of equation:

Y= A.D’+A.B’.C+A.B.C’+B.C’.D’